It is simply using the fact that two vectors are perpendicular if and only if their dot product is 0. Let be any fixed point and be any other point. Then the vector connecting them is [tex]<x- x_0, y- y_0, z- z_0>[tex] and the "set of all points such that the vector [tex]<x- x_0, y- y_0, z- z_0>[tex] is perpendicular to (the tangent plane to that vector containing ) must satisfy .